Question

The base radii of two right circular cones of same heights in the ratio 4:7. Find the ratio of their volume

Answer 1

$16:49\\</p><p><strong>Step-by-step</strong><strong>\</strong><strong>:</strong><strong> explanation:</strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong></p><p>ratio \: of \: base \: radii \:of \\2 \: right \: circular \: cones \: is \: 4:7 \\ \\they \: have \: equal \: heights \\ \\ Let \: the \: radius \: of \: 1st \: cone \: be \: 4x \\ \\ the \:radius \: of \: 2nd \: cone \: be \: 7x \\ \\ ratio \: of \: their \: volume = \frac{ \frac{1}{3} \pi {4x}^{2} \: h }{ \frac{1}{3}\pi {7x}^{2} \: h } \\ \\ = \frac{16 {x}^{2} }{49 {x}^{2} } = \frac{16}{49}=16:49$

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